Large-scale instability of a fine-grained turbulent jet |
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| Institution: | 1. Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287-6106, U.S.A.;2. Department of Applied Mathematics, Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, U.K.;1. State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi’an Jiaotong University, Xi’an 710049, China;2. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China;3. Guangxi Key Laboratory of Automobile Components and Vehicle Technology, Guangxi University of Science and Technology, Liuzhou 545006, China;4. Hubei Key Laboratory of Theory and Application of Advanced Materials Mechanics, Wuhan University of Technology, Wuhan 430070, China;1. TU Wien, Institute of Chemical, Environmental and Bioscience Engineering, Vienna, Austria;2. NovoArc GmbH, Vienna, Austria;1. Ostrom Workshop in Political Theory and Policy Analysis, Indiana University, 513 N. Park Avenue, Bloomington, IN 47408, United States;2. Department of Community Sustainability, Michigan State University, 131 Natural Resources Building, 480 Wilson Road, East Lansing, MI 48824, United States;1. Universidad Nacional de Colombia, Campus Bogotá, Department of Chemical and Environmental Engineering, Faculty of Engineering, Bogotá D.C. 111321, Colombia;2. Universidad Nacional de Colombia, Campus Bogotá, Department of Chemistry, Faculty of Sciences, Bogotá D.C. 111321, Colombia |
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| Abstract: | The initial growth of a large scale perturbation on a fine-grained turbulent jet is studied via linear stability analysis. The turbulent jet is assumed to be homogeneous and isotropic with zero mean shear, and the inviscid stream outside the jet has a uniform velocity profile. The incremental Reynolds stress caused by the large scale perturbation is modeled by a viscoelastic constitutive equation, following the analysis of Crow (1968). It is found that the jet is always unstable to both sinuous and varicose types of perturbation, with the sinuous mode having a larger growth rate. In particular, short waves are always amplified, in contrast to the short wave stabilization at low speed found by Townsend (1966) for a purely elastic jet. The growth rates of these short waves are finite, and are smaller than those for the classical Kelvin-Helmholtz instability of an inviscid jet, but larger than those for the Hooper-Boyd (1983) instability of a viscous jet with continuous velocity profile. |
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